hw11-3 - 254 4 Interest Rate Derivative Securities V ( r, T...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 254 4 Interest Rate Derivative Securities V ( r, T + )- V ( r, T- ) = Z T + T- V t dt =- Z T + T- ( t- T ) dt =- 1 . That is, V ( r, T- ) = V ( r, T + ) + 1 = 1 . In the first problem V ( r, T- ) = V ( r, T + ) is also identically equal to one. Consequently, from T- to any t < T , the solutions of the two problems are the same. Actually the second problem can be understood as another form of the first problem. 14. Consider the problem: V s 1 t + 1 2 w 2 2 V s 1 r 2 + ( u- w ) V s 1 r- rV s 1 + 2 N k =1 ( t- T- k/ 2) = 0 , r l r r u , t T + N, V s 1 ( r, T + N ) = 0 , r l r r u . Show that V s 1 ( r, T ) gives the sum of values of 2 N zero-coupon bonds with maturities 1 / 2 , 1 , 3 / 2 , , N years. Solution : The solution of the given problem is the sum of the solutions of the fol- lowing 2 N problems V s 1 k t + 1 2 w 2 2 V s 1 k r 2 + ( u- w ) V s 1 k r- rV s 1 k + ( t- T- k/ 2) = 0 , r l r r u , t T + N, V s 1 k ( r, T + N ) = 0 , r l r r u , k = 1 , 2 , , 2 N. It is clear that V s 1 k ( r, t ) = 0 for t ( T + k/ 2 , T + N ] and for t < T + k/ 2, V s 1 k ( r, t ) satisfies V s 1 k t + 1 2 w 2 2 V s 1 k r 2 + ( u- w ) V s 1 k r- rV s 1 k + ( t- T- k/ 2) = 0 , r l r r u , t T + k/ 2 , V s 1 k ( r, T + k/ 2) = 0 , r l r r u . 4 Interest Rate Derivative Securities 255 In Problem 13 we have shown that this problem can be rewritten as...
View Full Document

This note was uploaded on 02/11/2010 for the course MATH 6203 taught by Professor Zhu during the Spring '10 term at University of North Carolina Wilmington.

Page1 / 4

hw11-3 - 254 4 Interest Rate Derivative Securities V ( r, T...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online